OBAMA: I will not have another debate with this Congress over whether or not they should pay the bills.

MCCONNELL: It settled the revenue debate for good.

STEPHANOPOULOS: Will Washington hurdle off a higher cliff in just weeks? What can stop this cycle of brinksmanship? We'll ask our headliner, the senator at the center of this compromise, Republican Leader Mitch McConnell.

Then, as Speaker Boehner survives a close vote, fresh faces flood the Capitol. How will they change Congress? Will Congress change them? We introduce the rising stars of 2013.

Plus, a health scare for Hillary and that political storm over Hurricane Sandy.

ANNOUNCER: From ABC News, "This Week" with George Stephanopoulos. Reporting from ABC News headquarters, George Stephanopoulos.

(END VIDEO CLIP)

STEPHANOPOULOS: Hello again. Happy new year.

Even before President Obama's auto-pen signed this week's deal into law, it was clear that any cease-fire in Washington's battles over taxes and spending would be painfully brief.

Three new deadlines loom. By the end of February, the Treasury will lose the power to borrow more to pay America's bills. Across-the-board spending cuts to every federal program kick in on March 1st. And the government will run out of all congressional funding by the end of March. One fiscal cliff averted, three more coming fast.

And with that, let me turn to the man who negotiated last week's compromise with the White House, Senate Republican Leader Mitch McConnell.

Thank you for joining us, Senator.

MCCONNELL: Good morning, George.

STEPHANOPOULOS: So I know you think that the deal you negotiated is imperfect, so -- and you want to fix it, as we approach the debt limit. But I want to get to the bottom of this, because you say no increase in the debt limit without major cuts in spending. The president says he won't even negotiate over that. So to borrow General David Petraeus' famous quote from the Iraq war, how does this end?

MCCONNELL: Well, first, let me say these last-minute deals are no way to run the government. We've known all of these deadlines are coming. Why we end up in these last-minute discussions is beyond me. We need to function.

I mean, the House of Representatives, for example, passed a budget every year. They've passed appropriation bills. The Senate Democratic majority and the president seem to like these last-minute deals. Now, we know these three issues are coming up, the sequester, the debt ceiling, and the continuing resolution to operate the government. Why don't we sit down now and not wait until the last minute to get these matters resolved?